A labyrinth seal, at a minimum has to have enough clearance to permit the shaft to move however much the bearing clearances permit the shaft to move. Shafts move for a variety of reasons, bearing tolerances, or lubrication wedge thickness in the case of journal bearings, or vibrations, deflections in the pump, and more.
In any case, the shaft does not want to touch the seal, because that damages the seal, wearing off the sharpness of the teeth that is an integral part of the sealing process (sharped edge orifice concept) and creating hot spots that cause shaft bowing, causing more wiping, and more damage.
Inside of those parameters, they are used with great success in a variety of rotating machinery, pumps included.
If used with steam turbine drives, leaking steam from the turbine seals can enter the bearing cavity, so that has to be considered. This applies to any atmosphere surrounding the pump that would be detrimental to the internals of the bearing/lubrication system.
I hope this gives you a few details to ponder, while my peers come up with still more, maybe.
rmw